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Results tagged with ap.analysis-of-pdes
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user 147078
Partial differential equations (PDEs): Existence and uniqueness, regularity, boundary conditions, linear and non-linear operators, stability, soliton theory, integrable PDEs, conservation laws, qualitative dynamics.
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Notation for right hand side of local smoothing conjecture
In Tao's "Recent progress on the restriction conjecture"
On page 53, Tao introduced the local smoothing conjecture: let $u(t,x)$ be the solution to the wave equation $u_{tt}=\Delta u$, $u(0,x)=f(x)$ a …
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Pointwise convergence of Schrodinger's equation with potential term
A famous problem of Carleson asks if $f\in H^s(\mathbb{R}^n)$, under what condition of $s$ do we have almost everywhere pointwise convergence of the solution to the Schrodinger's equation
$$iu_t-\Delt …
- 265
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Mathematical study of dispersive PDEs [closed]
My understanding is that there have been a lot of activities in harmonic analysis and PDEs that use sophisticated tools to study dispersive PDEs like the Schrodinger's equation. E.g. the Strichartz es …
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